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Place a sieve over a medium bowl. Hold an orange over the bowl, and using a paring knife, cut along the membrane on both sides of each segment. Free the segments and let them fall into the sieve. Repeat with the grapefruit. Squeeze the membranes over the bowl to extract as much juice as possible, reserving the juices in the bottom of the bowl. Place the fruit segments and fennel in a salad bowl.

In a blender or the bowl of a small food processor, blend together the oil, basil and 3 tablespoons of the reserved juice until smooth. Season with salt and pepper, to taste. Pour over the fruit and fennel. Add the chopped walnuts and toss until all the ingredients are coated.